Choosing to go for a new job in the US, how to handle it?

[deusexlumina]

So at the place i work we have been contracted by another organisation for some time now (just over a year) and soon that work will be coming to an end.

I'd entertaining the possibility of asking them if they have any jobs on offer that i'd be suited to. However:

1. They are in the US
2. I don't want to annoy my current employer too much (burning bridges and all that)

Whats the best way to go about pursuing this possibility? Is it bad practise to talk about this kind of thing while we're still being asked by them to do other work?

If i go down this route, the job will be in the US. Anyone done this and have a view on how it was for them?

Thanks for any help

 

[deusexlumina]

Thanks for the replies guys. I'd heard of the visas, and i believe the deadline is in April which is why this is coming to a head all of a sudden and i feel i should ask about it.

With regards to the employment, they should be willing since its a reasonably specialised skill they're after (whether they accept me personally is another matter mind )

The whole client/customer thing is what i'm most concerned about i guess.